Path integrals are an indispensable computational tool in many areas of theoretical physics. Still today it is unclear how one can make full sense (according to standards of mathematical rigour) of the functional measure
\(\mathcal {D}[{r}(t)]\) , see Eq. (REF ). As is well known, a \(\sigma \) -additive Lebesque-type measure which is translationally and rotationally invariant does not exist in an Hilbert space of infinite dimensions. (See e. g. Ref.[1]}). Nevertheless, various attempts have been made at defining it in a more rigorous manner.[1]}, [3]}, [4]}, [5]}, [6]}Despite the lack of rigour its calculational power is remarkable. The actual situation bears some resemblance to the late 17th century when Leibniz' infinitesimals[7]} were applied successfully to various physico-mathematical issues despite their (at the time) rather obscure and mathematically ill-defined status. (See e. g. Ref.[8]})
